(1 point) Given $X' = AX$ with $X(t) = \begin{bmatrix} x(t) \\ y(t) \\ z(t) \end{bmatrix}$, $A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 3 & 3 \\ 0 & 3 & 0 \end{bmatrix}$ and $X(0) = \begin{bmatrix} 5 \\ -12 \\ -5 \end{bmatrix}$.
(a) Find the eigenvalues and eigenvectors of the matrix $A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 3 & 3 \\ 0 & 3 & 0 \end{bmatrix}$
$\lambda_1 = $____$, $X_1 = \begin{bmatrix} ____ \\ ____ \\ ____ \end{bmatrix}$
and
$\lambda_2 = $____$, $X_2 = \begin{bmatrix} ____ \\ ____ \\ ____ \end{bmatrix}$
